Question

[Dark Goddess]

So sánh

a) \(\dfrac{21}{52}\) và \(\dfrac{213}{523}\)

b) \(\dfrac{n}{n+1}\)và \(\dfrac{n+2}{n+3}\)

c) \(\dfrac{n}{n+3}\)và \(\dfrac{n-1}{n+4}\)

d) \(A=\dfrac{2^{2012}-1}{2^{2013}-1}\) và \(B=\dfrac{2^{2013}-1}{2^{2014}-1}\)

e) \(D=\dfrac{5^{12}+1}{5^{13}+1}\)và \(E=\dfrac{5^{11}+1}{5^{12}+1}\)

Answer 1

[Nguyễn Quang Ngọc Trác]

e, D = 5¹²+1 /5¹³+ 1 < 1 => 5¹²+1/ 5¹³+1 < 5¹²+1+4/ 5¹³+1+4

= 5¹²+5/ 5¹³+5 = 5. (5¹¹+1) / 5. (5¹²+1) = 5¹¹+1 / 5¹²+1= E

Vậy D < E